Answer: (0, 3)
Explanation:
You need to put the equation in the circle formula. In order to do that, you need to complete the square.
(x-h)² +(y-k)² = r² where (h,k) is the center
Your equation:
x²+y²-6y-16 = 0 bring over constants to other side
x²+y²-6y = 16 complete the square by taking the y term (6) divide by 2 and square that number to add to both sides
= 3² = 9 this is the completion of square for the y quadratic part
add to both sides of equation
x²+y²-6y+9= 16 +9
x²+y²-6y +9= 25 factor the y quadratic part
you get (y-3)(-3) = (y-3)²
x²+(y-3)² = 16 we have put it in the format above (x-h)² +(y-k)² = r²
there is no x so h=0 k=3
so the center is (0,3)